00:01
In this problem, we have an object and that object is having mass of 8 kilograms and it's moving on a surface which provides the friction so that it comes to rest after traveling 10 meters.
00:17
And it's observed that the initial speed was 4 meter per second.
00:22
So as it comes to rest, finally its speed will drop to 0 meter per second.
00:27
And now we have to determine the distance that this object will travel if the initial speed is doubled.
00:37
So for that, let's compute the acceleration here.
00:41
And as we can see that, the speed is changing.
00:44
So here the work that's done by the friction, that will be the network done, which will bring this change in the kinetic energy.
00:54
So using the work energy theorem, that's the network done, is the change.
00:58
In kinetic energy, we see that the work done by friction, it's negative, and that will be the friction force multiplied with the distance, and that's 10 here in this first case, and it's negative, and that's equal to the change in kinetic energy, which is the final kinetic energy, that's zero, because the block comes to rest minus the initial kinetic energy, that's half times the mass of this block times the square of initial speed.
01:29
And from here we get the friction force, which is 8 times 4 square divided by 2, that's 4 cube over 10.
01:38
So that's 6 .4 newtons...